Free space single-mode fibers and fiber components for fiber sensor applications

ABSTRACT

This invention relates to a near real time optical compensation verification system for verifying a fiber or fiber component through internal or external compensation to achieve equivalently free space propagation of a broadband light when coupled into fiber. Preferably, no component is added to the fiber or fiber component, and the compensation method is realized through real time fiber bending, twisting or other means at either or both ends of a fiber or fiber component. The output optical characteristics of the compensated fiber or fiber component are measured by a polarimeter through changing the input light properties. The required multi-variable compensation to achieve Unitary Matrix free space condition is computed in near real time, and as the feedback to formulate the required compensation. The disclosed invention not only enhances yield in the fiber and fiber component, but also accelerates the optimization of optical fiber sensors employed free space fiber coil.

CROSS REFERENCE TO RELATED APPLICATION(S)

This application is a division of U.S. patent application Ser. No.13/149,208, filed May 31, 2011, claiming foreign priority as well toTW-100102012, filed on Jan. 19, 2011, which is/are incorporated byreference as if fully set forth.

FIELD OF THE INVENTION

The invention relates to a compensation method for a fiber or a fibercomponent. More particularly this invention is to compensate the changesof optical characteristics for the light in a fiber or a fiber componentsuch as a fiber coil of the optical fiber sensor (for example, the fiberoptic gyros). The compensation method not only makes the opticalcharacteristics of each fiber or fiber component like as the free spacebut also greatly accelerate the design simulation for optical circuitoptimization of optical fiber sensors.

BACKGROUND OF THE INVENTION

In our daily life, the role of optical fiber technology is getting moreand more important. The sensitivity, stability and reproducibility offiber components are more important when they are applied in thenavigation, orientation and platform stability technologies. Because themanufacture process of fiber components (e.g. fiber coil) causes fiber'soptical property change and loss, it will make the function of fibercomponents reduce and degrade.

In the prior art, several different strategies (US 2003/0007751A1-US2005/0226563A1) are used to solve the problem in optical property changeor loss in optical fiber elements. For example, thepolarization-maintaining (PM) fiber can be applied to keep thepolarization state of light, but the cost of PM fiber is high.Furthermore, the PM fiber ring around the coil is required to maintainthe polarization extinction ratio, and this parameter is not easy tomaintain. Thus it will increase the cost and difficulty in themanufacture process. Also, the quality of fiber coil is easily affectedeasily by fiber quality, stress and strain in the winding process, andthe rubber filled in the fiber coil. As a result, every fiber coil mayproduce different levels of optical properties such as linearbirefringence (LB), linear diattenuation (LD) and circular birefringence(CB) characteristics or their combination.

For a long time, the high-quality fiber coil winding process in fibergyroscopes is a high-tech process. It requires not only the combinationof special optical fiber and automatic tension control machines, butalso the machine under a highly experienced mechanic operation in orderto control the quality of fiber coil in an acceptable rage. Thus thehigh-tech process in fiber coil causes the production costs extremelyhigh. If the quality of fiber coil (from different production dates ordifferent plants) is uncontrollable, the fiber coil winding processneeds additional time-consuming tests by re-adjusting fiber coil withinthe scope of the best quality. If you bypass this adjusting in fibercoil, the poor fiber coils are forced to the lower level in business.Thus the yield of high-quality fiber coil will be substantially reduced.

According to the present invention, applicants have departed from theconventional wisdom, and had conceived and implemented the free spacesingle-mode fibers for fiber sensor, which is relative to that ofcompensating the fiber or fiber component such that the fiber or fibercomponent plus the compensated optical circuit act as if an UnitaryMatrix free space condition. The disclosed free space single-mode fiberinvention not only greatly enhances repeatability in the fiber and fibercomponent production line, it also can be employed to accelerate thedesign simulation for optical circuit optimization of optical fibersensors. Such a fast simulation and the compensated optical circuitnearly acted as if a free space are unprecedented in open literature.The invention is briefly described as follows.

SUMMARY OF THE INVENTION

In the prior act, the equivalent parameters represented the opticalcircuit can be obtained by the Mueller-Stokes Matrix (Characterizationon five effective parameters of anisotropic optical material usingStokes parameters-Demonstration by a fiber-type polarimeter, OpticsExpress, Vol. 18, Issue 9, pp. 9133-9150, April 2010). Please refer toFIG. 1, which shows the experiment environment in the prior art. Thepolarized light provided by the laser 100 passes through thequarter-wave plate 101 and the polarizer 102 in order to generate fourlinear polarized lights (0°, 45°, 90° and 135°) and two circuitpolarized lights (left spin and right spin), and then the six polarizedlights are input into the sample fiber 103. After that, the sixpolarized lights output from the sample fiber 103 and input the MuellerStokes Matrix polarimeter 104 for measuring the polarization states ofthe six polarized light.

Then, the five equivalent parameters represented the sample fiber 103, aprincipal axis angle (α), a phase retardation (β), a diattenuation axisangle (θ_(d)), a diattenuation (D) and the optical rotation angle (γ),are obtained by inverting the polarization states of the six polarizedlight measured from the Mueller Stokes Matrix polarimeter 104. Thedynamic range for the five parameters a, β, θ_(d), D and γ is measuredin 0°˜180°, 0°˜180°, 0°˜180°, 0˜1 and 0°˜180°, respectively.

The Stokes vectors are used to represent the polarization state of thelight as follows:

$\begin{matrix}{S = {\begin{bmatrix}S_{0} \\S_{1} \\S_{2} \\S_{3}\end{bmatrix} = \begin{bmatrix}{I_{x} + y} \\{I_{x} - I_{y}} \\{I_{45^{{^\circ}}} - I_{- 45^{{^\circ}}}} \\{I_{RHC} - I_{LHC}}\end{bmatrix}}} & (1.1)\end{matrix}$

where I_(x) and I_(y) is the intensity of the horizontal and verticalpolarized light, respectively, I₄₅ ⁰ and I⁻⁴⁵ ⁰ is the intensity of the45° and −45° polarized light, respectively, I_(RIIC) and I_(LIIC) is theintensity of the left spin and right spin polarized light, respectively,S₀ is the total intensity of the light, S ₁ is the difference of theintensity of the horizontal and vertical polarized light, S₂ is thedifference of the intensity of the 45° and −45° polarized light and S₃is the difference of the intensity of the left spin and right spinpolarized light. The Mueller Stokes Matrix polarimeter 104 can measurethe polarization state of the light, i.e., four Stokes parameters.

The 4×4 Mueller Matrix is used to represent the optical component whichchanges the polarization state of the light. According to FIG. 1, thepolarization state (s) of the outputting light are obtained bymultiplying the polarization state (Ŝ) of the inputting light by thematrix of the equivalent optical parameters (M) of the fiber component,as follows:

$\begin{matrix}\begin{matrix}{S = \begin{bmatrix}S_{0} \\S_{1} \\S_{2} \\S_{3}\end{bmatrix}} \\{= {\begin{pmatrix}m_{11} & m_{12} & m_{13} & m_{14} \\m_{21} & m_{22} & m_{23} & m_{24} \\m_{31} & m_{32} & m_{33} & m_{34} \\m_{41} & m_{42} & m_{43} & m_{44}\end{pmatrix}\begin{pmatrix}{\hat{S}}_{0} \\{\hat{S}}_{1} \\{\hat{S}}_{2} \\{\hat{S}}_{3}\end{pmatrix}}} \\{= {M\hat{S}}}\end{matrix} & (1.2)\end{matrix}$

and the Mueller Matrix M is:

$\begin{matrix}{M = \begin{pmatrix}m_{11} & m_{12} & m_{13} & m_{14} \\m_{21} & m_{22} & m_{23} & m_{24} \\m_{31} & m_{32} & m_{33} & m_{34} \\m_{41} & m_{42} & m_{43} & m_{44}\end{pmatrix}} & (1.3)\end{matrix}$

where m_(ij), i, j=1, 2, 3 and 4, is the equivalent optical parametersof the fiber component.

The Jones Matrix (U) of the optical component is:

$\begin{matrix}{U = \begin{bmatrix}u_{11} & u_{12} \\u_{21} & u_{22}\end{bmatrix}} & (1.4)\end{matrix}$

where u_(ij), i, j=1 and 2 is the equivalent optical parameters of thefiber component.

The Mueller Matrix represented the optical component is obtained via thefollowing transformation formula:

M=T(U{circle around (×)} U*)T ⁻¹ S   (1.5)

where U is the Jones Matrix, S is the polarization state (Ŝ) of theinputting light, T is a matrix described as follows:

$\begin{matrix}{T = \begin{pmatrix}1 & 0 & 0 & 1 \\1 & 0 & 0 & {- 1} \\0 & 1 & 1 & 0 \\0 &  & {- } & 0\end{pmatrix}} & (1.6)\end{matrix}$

and the matrix U{circle around (×)}U* is described as follows:

$\begin{matrix}{{U \otimes U^{*}} = \begin{pmatrix}{u_{11}u_{11}^{*}} & {u_{11}u_{12}^{*}} & {u_{12}u_{11}^{*}} & {u_{12}u_{12}^{*}} \\{u_{11}u_{21}^{*}} & {u_{11}u_{22}^{*}} & {u_{12}u_{21}^{*}} & {u_{12}u_{22}^{*}} \\{u_{21}u_{11}^{*}} & {u_{21}u_{12}^{*}} & {u_{22}u_{11}^{*}} & {u_{22}u_{12}^{*}} \\{u_{21}u_{21}^{*}} & {u_{21}u_{22}^{*}} & {u_{22}u_{21}^{*}} & {u_{22}u_{22}^{*}}\end{pmatrix}} & (1.7)\end{matrix}$

In the present invention, the fiber is assumed to have the linearbirefringence, linear diattenuation and circular birefringence. Firstly,in the case of the fiber having the linear birefringence of theprincipal axis angle (α) and retardance (β), whose Jones Matrix U_(b) isdescribed as follows:

$\begin{matrix}{U_{b}\begin{matrix}{= {{\begin{bmatrix}{\cos (\alpha)} & {- {\sin (\alpha)}} \\{\sin (\alpha)} & {\cos (\alpha)}\end{bmatrix}\begin{bmatrix}{\exp \left( {{- }\frac{\beta}{2}} \right)} & 0 \\0 & {\exp \left( {\frac{\beta}{2}} \right)}\end{bmatrix}}\begin{bmatrix}{\cos (\alpha)} & {\sin (\alpha)} \\{- {\sin (\alpha)}} & {\cos (\alpha)}\end{bmatrix}}} \\{= \begin{bmatrix}{{\cos \left( \frac{\beta}{2} \right)} - {\; {\cos \left( {2\alpha} \right)}{\sin \left( \frac{\beta}{2} \right)}}} & {{- }\; {\sin \left( {2\alpha} \right)}{\sin \left( \frac{\beta}{2} \right)}} \\{{- }\; {\sin \left( {2\alpha} \right)}{\sin \left( \frac{\beta}{2} \right)}} & {{\cos \left( \frac{\beta}{2} \right)} + {\; {\cos \left( {2\alpha} \right)}{\sin \left( \frac{\beta}{2} \right)}}}\end{bmatrix}}\end{matrix}} & (1.8)\end{matrix}$

So, the Mueller Stokes Matrix of the fiber having the linearbirefringence is described as the following equation (1.9):

$M_{lb} = \begin{pmatrix}1 & 0 & 0 & 0 \\0 & {{{\cos \left( {4\alpha} \right)}{\sin^{2}\left( {\beta/2} \right)}} + {\cos^{2}\left( {\beta/2} \right)}} & {{\sin \left( {4\alpha} \right)}{\sin^{2}\left( {\beta/2} \right)}} & {{\sin \left( {2\alpha} \right)}{\sin (\beta)}} \\0 & {{\sin \left( {4\alpha} \right)}{\sin^{2}\left( {\beta/2} \right)}} & {{{- {\cos \left( {4\alpha} \right)}}{\sin^{2}\left( {\beta/2} \right)}} + {\cos^{2}\left( {\beta/2} \right)}} & {{- {\cos \left( {2\alpha} \right)}}{\sin (\beta)}} \\0 & {{- {\sin \left( {2\alpha} \right)}}{\sin (\beta)}} & {{\cos \left( {2\alpha} \right)}{\sin (\beta)}} & {\cos (\beta)}\end{pmatrix}$

Secondly, in the case of the fiber having the linear diattenuation ofthe diattenuation axis angle (θ_(d)) and the transmission rates u and v,whose Jones Matrix U_(d) is described as follows:

$\begin{matrix}\begin{matrix}{U_{d} = {{\begin{bmatrix}{\cos \left( \theta_{d} \right)} & {- {\sin \left( \theta_{d} \right)}} \\{\sin \left( \theta_{d} \right)} & {\cos \left( \theta_{d} \right)}\end{bmatrix}\begin{bmatrix}\sqrt{u} & 0 \\0 & \sqrt{v}\end{bmatrix}}\begin{bmatrix}{\cos \left( \theta_{d} \right)} & {\sin \left( \theta_{d} \right)} \\{- {\sin \left( \theta_{d} \right)}} & {\cos \left( \theta_{d} \right)}\end{bmatrix}}} \\{= \begin{bmatrix}{{\sqrt{u}{\cos^{2}\left( \theta_{d} \right)}} + {\sqrt{v}{\sin^{2}\left( \theta_{d} \right)}}} & {\left( {\sqrt{u} - \sqrt{v}} \right){\cos \left( \theta_{d} \right)}{\sin \left( \theta_{d} \right)}} \\{\left( {\sqrt{u} - \sqrt{v}} \right){\cos \left( \theta_{d} \right)}{\sin \left( \theta_{d} \right)}} & {{\sqrt{u}{\sin^{2}\left( \theta_{d} \right)}} + {\sqrt{v}{\cos^{2}\left( \theta_{d} \right)}}}\end{bmatrix}}\end{matrix} & (1.10)\end{matrix}$

So, the Mueller Stokes Matrix of the fiber having the lineardiattenuation is described as the following equation (1.11):

$\begin{matrix}{M_{ld} = \begin{pmatrix}\frac{\left( {u + v} \right)}{2} & \frac{{\cos \left( {2\; \theta_{d}} \right)}\left( {u,v} \right)}{2} & \frac{{\sin \left( {2\; \theta_{d}} \right)}\left( {u - v} \right)}{2} & 0 \\\frac{{\cos \left( {2\; \theta_{d}} \right)}\left( {u - v} \right)}{2} & \begin{matrix}{\frac{\left( {\sqrt{u} + \sqrt{v}} \right)^{2}}{4} +} \\\frac{{\cos \left( {4\; \theta_{d}} \right)}\left( {\sqrt{u} - \sqrt{v}} \right)^{2}}{4}\end{matrix} & \frac{{\sin \left( {4\; \theta_{d}} \right)}\left( {\sqrt{u} - \sqrt{v}} \right)^{2}}{4} & 0 \\\frac{{\sin \left( {2\; \theta_{d}} \right)}\left( {u - v} \right)}{2} & \frac{{\sin \left( {4\; \theta_{d}} \right)}\left( {\sqrt{u} - \sqrt{v}} \right)^{2}}{4} & \begin{matrix}{\frac{\left( {\sqrt{u} + \sqrt{v}} \right)^{2}}{4} -} \\\frac{{\cos \left( {4\; \theta_{d}} \right)}\left( {\sqrt{u} - \sqrt{v}} \right)^{2}}{4}\end{matrix} & 0 \\0 & 0 & 0 & \sqrt{uv}\end{pmatrix}} & \;\end{matrix}$

The diattenuation D is described as follows:

$\begin{matrix}{{D = \frac{u - v}{u + v}}{and}} & (1.12) \\{e = \frac{1 - D}{1 + D}} & (1.13)\end{matrix}$

where e is v/u, so that (1.10) and (1.11) are respectively described asthe following equations (1.14) and (1.15):

$\begin{matrix}\begin{matrix}{U_{d} = {{\begin{bmatrix}{\cos \left( \theta_{d} \right)} & {- {\sin \left( \theta_{d} \right)}} \\{\sin \left( \theta_{d} \right)} & {\cos \left( \theta_{d} \right)}\end{bmatrix}\begin{bmatrix}1 & 0 \\0 & \sqrt{\frac{1 - D}{1 + D}}\end{bmatrix}}\begin{bmatrix}{\cos \left( \theta_{d} \right)} & {\sin \left( \theta_{d} \right)} \\{- {\sin \left( \theta_{d} \right)}} & {\cos \left( \theta_{d} \right)}\end{bmatrix}}} \\{= \begin{bmatrix}\begin{matrix}{{\cos^{2}\left( \theta_{d} \right)} +} \\{\sqrt{\frac{1 - D}{1 + D}}{\sin^{2}\left( \theta_{d} \right)}}\end{matrix} & \begin{matrix}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right) \\{{\cos \left( \theta_{d} \right)}{\sin \left( \theta_{d} \right)}}\end{matrix} \\\begin{matrix}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right) \\{{\cos \left( \theta_{d} \right)}{\sin \left( \theta_{d} \right)}}\end{matrix} & \begin{matrix}{{\sin^{2}\left( \theta_{d} \right)} +} \\{\sqrt{\frac{1 - D}{1 + D}}{\cos^{2}\left( \theta_{d} \right)}}\end{matrix}\end{bmatrix}}\end{matrix} & (1.14)\end{matrix}$

and equation (1.15):

$M_{ld} = \begin{pmatrix}\frac{\left( {1 + \frac{1 - D}{1 + D}} \right)}{2} & \frac{{\cos \left( {2\; \theta_{d}} \right)}\left( {1 - \frac{1 - D}{1 + D}} \right)}{2} & \frac{{\sin \left( {2\; \theta_{d}} \right)}\left( {1 - \frac{1 - D}{1 + D}} \right)}{2} & 0 \\\frac{{\cos \left( {2\; \theta_{d}} \right)}\left( {1 - \frac{1 - D}{1 + D}} \right)}{2} & \begin{matrix}{\frac{\left( {1 + \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4} +} \\\frac{{\cos \left( {4\; \theta_{d}} \right)}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4}\end{matrix} & \frac{{\sin \left( {4\; \theta_{d}} \right)}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4} & 0 \\\frac{{\sin \left( {2\; \theta_{d}} \right)}\left( {1 - \frac{1 - D}{1 + D}} \right)}{2} & \frac{{\sin \left( {4\; \theta_{d}} \right)}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4} & \begin{matrix}{\frac{\left( {1 + \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4} -} \\\frac{{\cos \left( {4\; \theta_{d}} \right)}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4}\end{matrix} & 0 \\0 & 0 & 0 & \sqrt{\frac{1 - D}{1 + D}}\end{pmatrix}$

Finally, in the case of the fiber having the circular birefringence ofthe optical rotation angle (γ), whose Jones Matrix U_(cb) is describedas follows:

$\begin{matrix}{U_{cb} = \begin{bmatrix}{\cos (\gamma)} & {\sin (\gamma)} \\{- {\sin (\gamma)}} & {\cos (\gamma)}\end{bmatrix}} & (1.16)\end{matrix}$

So, the Mueller Stokes Matrix of the fiber having the circularbirefringence is described as follows:

$\begin{matrix}{M_{cb} = \begin{pmatrix}1 & 0 & 0 & 0 \\0 & {\cos \left( {2\; \gamma} \right)} & {\sin \left( {2\; \gamma} \right)} & 0 \\0 & {- {\sin \left( {2\; \gamma} \right)}} & {\cos \left( {2\; \gamma} \right)} & 0 \\0 & 0 & 0 & 1\end{pmatrix}} & (1.17)\end{matrix}$

According to the above description, the equivalent parametersrepresented the optical circuit of the single-mode fiber and opticalfiber component such as the fiber coil can be represented by the MuellerStokes Matrix via the measurement of the Mueller Stokes Matrixpolarimeter.

The present invention is proposed to measure the equivalent optical pathof optical components or optical fiber such as fiber coil, and thencompensate for it to become a free space unit matrix. So that thestability and reproducibility of optical components or optical fibersuch as fiber coil in a fiber gyroscope can be promoted. The theoreticalcalculation is that Mueller Stokes polarimeter is applied to analyze theresults, and then design and calculate the compensation for opticalfiber or optical components in order to convert their matrix into thefree-space unit matrix.

The fiber sensor provided by the present invention is composed byoptically connecting a light source, the optical components, a fiber orfiber component and a light detector. And the polarization state of thelight passing through the fiber or fiber components is compensated by acompensation method.

Preferably, the compensation method is performed by adding a variableretarder and a half-wave plate and etc, and a polarization controllercan be used to replace the variable retarder and the half-wave plate.

Preferably, no component is added, and the compensation method isrealized through fiber bending, twisting or other means at either orboth ends of a fiber or fiber component.

According to the method provided by the present invention, thecalculated compensation can recover the changes of the opticalcharacteristics of the light passing through the fiber or fibercomponent caused by the environment and the fabrication process.Compared to the prior art, the invention is performed with adding theoptical component or without adding the optical component to remain thepolarization state of the inputting light. It also can be employed togreatly accelerate the design simulation for optical circuitoptimization of optical fiber sensors due to the compensated opticalcircuit is a free space unit matrix. As a result, such a fast simulationand the nearly complete recovery of the optical characteristic(excepting the optic power loss) lead to that the optical fiberapparatus made by compensation method can be applied for optical fibersensors fabricated by fiber and fiber component such as fiber opticgyros, including navigation, orientation, platform stabilization andetc.

In accordance with further aspect of the present invention, an opticalsystem is provided. The optical system includes an optical circuit forpropagating a light and an optical compensation assembly placed on theoptical circuit to compensate the changes of optical characteristics ofthe light after the light passing through the optical circuit. Thecompensation is based on a compensation method of transformation matrix.

In summary, the present invention has disclosed a compensation method tomake the equivalent optical circuit of the compensated fiber or fibercomponent act as if an Unitary Matrix free space condition aftermeasuring the fiber and fiber component. Especially, the resultsobtained from the Mueller Matrix polarimeter are analyzed theoreticallyto calculate the compensation when the equivalent Jones Matrixrepresented the fiber or fiber component such as a fiber coil istransformed to the unit matrix represented the free space. The recoveryof optical characteristics is reached by the compensation method viaadding optical components or no optical components added. And we furtherprovide an optical verification method to verify the equivalent opticalcircuit of the compensated fiber or fiber component.

The above aspects and advantages of the present invention will becomemore readily apparent to those ordinarily skilled in the art afterreviewing the following detailed descriptions and accompanying drawings,in which:

BRIEF DESCRIPTION OF THE DRAWINGS AND TABLES

FIG. 1 shows the schematic diagram of simulation architecture of aMueller Stoke Matrix in the prior art;

FIG. 2( a) is a first preferred implementation case schematic diagram ofthe present invention, which is used to verify the accuracy of fiber'sfive optical parameters;

FIG. 2( b) is the implementation of the proposed verification method inthe present invention, which is used to verify the accuracy of fiber'sfive optical parameters;

FIG. 2( c) shows the comparison of principal axis angle and retardancebetween the known optical parameters of a quarter-wave plate and opticalparameters extracted by using the proposed verification method;

FIG. 3( a) shows the schematic diagram of free-space unit matrix;

FIG. 3( b) is the comparison of azimuth angles and ellipticity angles ofinput/output lights given input lights with different linearpolarization states;

FIG. 3( c) is the comparison of azimuth angles and ellipticity angles ofinput/output lights given input lights with randomly-chosen right- andleft-hand elliptical polarization states;

FIG. 3( d) is the comparison of azimuth angles and ellipticity angles ofinput/output lights given input lights with different linearpolarization states using a broadband light source;

FIG. 3( e) is the comparison of azimuth angles and ellipticity angles ofinput/output lights given input lights with randomly-chosen right- andleft-hand elliptical polarization states using a broadband light source;

FIGS. 4( a) and (b) are a second and third preferred implementation caseschematic diagrams of the present invention, respectively, which showthe compensated fiber coils;

TABLE 1. is the comparison of Ellipticity Angles of Input/Output LightsGiven Input Lights with Right- and Left-Hand Circular PolarizationStates; and

TABLE 2. is the comparison of ellipticity angles of input/output lightsgiven input lights with right- and left-hand circular polarization stateusing a broadband light source.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention will now be described more specifically withreference to the following embodiments. It is to be noted that thefollowing descriptions of preferred embodiments of this invention arepresented herein for the purposes of illustration and description onlyit is not intended to be exhaustive or to be limited to the precise formdisclosed.

Please refer to FIG. 2( a), which is the first better implementationexample for this case. It is a schematic diagram in compensating forfiber 203. FIG. 2( a) illustrates two fiber coupling devices 202 that isused to connect an optical fiber 203. The polarizer 206 and thequarter-wave plate 207 is used to produce linearly polarization lightand neutral density filter 205 and power meter detector 204 is used toensure that each of the input lights has an identical intensity.Finally, the polarization state of input light can be measured by Stokespolarimeter 201.

In order to measure five effective optical parameters in a fiber coil, a1000 m in length of single mode fiber 203 is used for measurement. FIG.2( b) illustrates two fiber coupling devices 202 that is used to connectan optical fiber 203. The polarizer 206 and the quarter-wave plate 207is used to produce linearly polarization light and neutral densityfilter 205 and power meter detector 204 is used to ensure that each ofthe input lights has an identical intensity. The single mode fiber 203is wound on a plastic cylinder which diameter is 15 cm. And the lightsource 200 is a broadband light source such as ASE (1520 nm˜1570 nm) Bythe different combinations of principal angle of polarizer 206 andquarter-wave plate 207, it can produce four linear polarization lights(0°, 45°, 90 °, 135°) and two circular polarization lights (left andright hand). The Stokes polarimeter 201 is applied to measure the Stokesparameters after the different polarization states of light throughoptical fiber 203, respectively. The following method to compute thesingle model optical fiber coil's five equivalent parameters isintroduced.

The four linear polarization lights: Ŝ_(0°)=[1, 1, 0, 0], Ŝ_(45°)=[1, 0,1, 0], Ŝ_(90°)=[1, −1, 0, 0] and Ŝ_(135°)=[1, 0, −1, 0] and two circularpolarization lights: right handed Ŝ_(RHC)=[1, 0, 0, 1] and left handedŜ_(LHC)=[1, 0, 0, −1] are going through the sample, respectively. Inbelow equations, S₀ is the total light intensity, S₁ is the intensitydifference between the horizontal and vertical linearly polarizedcomponents, S₂ is the intensity difference between the linearlypolarized components oriented at ±45°, and S₃ is the intensitydifference between the right- and left-hand circularly polarizedcomponents.

As a result, the term 2α+2γ of the sample can be obtained as

$\begin{matrix}{{{2\; \alpha} + {2\; \gamma}} = {\tan^{- 1}\left( \frac{- {S_{0{^\circ}}\left( S_{3} \right)}}{S_{45{^\circ}}\left( S_{3} \right)} \right)}} & (2.19)\end{matrix}$

After determining 2α+2γ, the retardance can be obtained as

$\begin{matrix}{\beta = {\tan^{- 1}\left( \frac{S_{45 \circ}\left( S_{3} \right)}{{\cos \left( {{2\; \alpha} + {2\; \gamma}} \right)} \cdot {S_{RH}\left( S_{3} \right)}} \right)}} & (2.20)\end{matrix}$

-   The diattenuation axis θ_(d) can be expressed as

$\begin{matrix}{{2\; \theta_{d}} = {\tan^{- 1}\left( \frac{{S_{45{^\circ}}\left( S_{2} \right)} + {S_{135{^\circ}}\left( S_{2} \right)}}{{S_{0{^\circ}}\left( S_{1} \right)} + {S_{90{^\circ}}\left( S_{1} \right)}} \right)}} & (2.21)\end{matrix}$

The Diattenuation D can be expressed as

$\begin{matrix}{D = \frac{{S_{45{^\circ}}\left( S_{2} \right)} + {S_{135{^\circ}}\left( S_{2} \right)}}{{\sin \left( {2\; \theta_{d}} \right)} \cdot \left\lbrack {{S_{0{^\circ}}\left( S_{0} \right)} + {S_{90{^\circ}}\left( S_{0} \right)}} \right\rbrack}} & (2.22)\end{matrix}$

The principal axis 2α can be expressed as

${2\; \alpha} = {\tan^{- 1}\left( \frac{{C_{3}\left\lbrack {{S_{RHC}\left( S_{2} \right)} - {S_{LHC}\left( S_{2} \right)}} \right\rbrack} - {C_{2}\left\lbrack {{S_{RHC}\left( S_{3} \right)} - {S_{LHC}\left( S_{3} \right)}} \right\rbrack}}{{C_{2}\left\lbrack {{S_{RHC}\left( S_{2} \right)} - {S_{LHC}\left( S_{2} \right)}} \right\rbrack} - {C_{1}\left\lbrack {{S_{RHC}\left( S_{3} \right)} - {S_{LHC}\left( S_{3} \right)}} \right\rbrack}} \right)}$

where

$\begin{matrix}{C_{1} = {\left( {\frac{\left( {1 + \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4} + \frac{{\cos \left( {4\; \theta_{d}} \right)}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4}} \right){\sin (\beta)}}} & (2.24) \\{C_{2} = {\left( \frac{{\sin \left( {4\; \theta_{d}} \right)}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4} \right){\sin (\beta)}}} & (2.25) \\{C_{3} = {\left( {\frac{\left( {1 + \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4} - \frac{{\cos \left( {4\; \theta_{d}} \right)}\left( {1 - \sqrt{\frac{1 - D}{1 + D}}} \right)^{2}}{4}} \right){\sin (\beta)}}} & (2.26)\end{matrix}$

Then, 2γ can be obtained as

$\begin{matrix}{{2\; \gamma} = {{\tan^{- 1}\left( \frac{- {S_{0{^\circ}}\left( S_{3} \right)}}{S_{45{^\circ}}\left( S_{3} \right)} \right)} - {2\; \alpha}}} & (2.27)\end{matrix}$

Then, we can extract five effective optical parameters of α, β, θ_(d),D, and γ of the SM fiber coil are 71.92°, 144.98°, 96.11°, 0.041°,23.67, respectively.

Please refer to FIG. 2( b), and this is the proposed verification methodof implementation example for this invention. To verify the accuracy offiber's five optical parameters, we use the extracted five effectiveoptical parameters to measure the known linear birefringence sample. Thelinear birefringence sample is a quarter-wave plate 208. The knownretardance is 90° and slow axis of quarter-wave plate 211 in the back ofan optical fiber is rotated in 0°, 30°, 60°, 90°, 120° and 150° formeasurement of LB sample in various angles. If the values of fiveoptical parameters in SM fiber are correct, the known principal axes andretardance of quarter-wave plate 208 can be obtained correctly.

Please refer to FIG. 2( c), and it shows the comparison of principalaxis angle and retardance between the known optical parameters of aquarter-wave plate 211 and optical parameters extracted by using themethod above. The experimental results show that the extracted values ofthe principal axis angle and retardance of the quarter-wave plate haveaverage absolute error of α_(S)=1.42° and β_(S)=4.03°, respectively.From above results, the extracted five effective optical parameters cancorrectly represent the optical properties of the single-mode fibercoil.

Please refer to FIG. 3( a), and it shows a variable retarder (VR) andhalf-wave plate (HP) are inserted between the power meter and the fibercoupler used to couple the input polarization light into the opticalfiber (referring to “Design of Polarization-Insensitive Optical FiberProbe Based on Effective Optical Parameters”, JOURNAL OF LIGHTWAVETECHNOLOGY, VOL. 29, NO. 8, APR. 15, 2011). The VR compensates for theLB property of the fiber, while the HP compensates for the CB property.Thus, through an appropriate setting of the principal axis angle andretardance of the VR, and the optical rotation of the HP, the opticalfiber can be converted into a free-space medium with negligible linearor circular birefringence. The free-space unit matrix of the VR/HP/fiberconfiguration shown in FIG. 3( a) can be formulated as follows:

$\begin{matrix}{{{\left\lbrack M_{Fiber} \right\rbrack \left\lbrack M_{HP} \right\rbrack}\left\lbrack M_{VR} \right\rbrack} = \begin{pmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{pmatrix}} & (2.28)\end{matrix}$

Therefore, it follows that

[M _(HP) ][M _(VR) ]=[M _(Fiber)]⁻¹   (2.29)

where [M_(Fiber)]=[M_(ld)][M_(lb)][M_(cb)]≈[M_(lb)][_(cb)] since[M_(id)]≈[1], and thus [M_(HP)]≈[M_(cb)]⁻¹ and [M_(VR)]≈[M_(lb)]⁻¹. Notethat [M_(HP)] is the Mueller matrix of the HP , and has one variableparameter, (γ_(H)). [M_(VR)] is the Mueller matrix of the VR, and hastwo variable parameters, (α_(v) and β_(v)). [M_(Fiber)] is the Muellermatrix of the optical fiber, and has three constant parameters, (α, βand γ). Generally speaking, the values of α_(v), β_(v) and γ_(H)required to compensate for the birefringence properties of the opticalfiber are determined via an experimental trial-and-error process.However, this process is tedious and time-consuming Furthermore, itcannot absolutely guarantee the formation of a free-space condition.Accordingly, in the prior art, a method is proposed for determining theoptimal values of α_(v), β_(v) and γ_(H) for any optical fiber or fiberconfiguration using a genetic algorithm.

According to this implementation example, if a free-space unit matrix isfinally achieved, the input polarization states into the compensationfiber are exactly same as the output polarization states. The lighttraveling in a free-space fiber is just like light traveling in air. AHe—Ne laser (SL 02/2, SIOS Co.) with a central wavelength of 632.8 nm isuesd to produce linear input polarization lights.

Please refer to FIG. 3( b), it is seen that the azimuth angle of theoutput light is linearly correlated with the azimuth angle of the inputlight for all linear polarization states. Furthermore, the ellipticityangle of the output light is equal to approximately zero for all anglesof the linear polarized light. FIG. 3( b) confirm that the azimuth andellipticity angles of the light emerging from the VR/HP/fiber structureare virtually identical to those of the light entering the VR. In otherwords, a free-space condition is successfully achieved when using theoptimal VR and HP settings determined by the GA. FIG. 3( b) for linearinput polarization lights, a further series of experiments was performedto evaluate its feasibility given right-hand and left-hand circularinput polarization lights, respectively. The results presented in Table1 confirm that a good agreement exists between the ellipticity angles ofthe input and output lights in both polarization states.

Please refer to FIG. 3( c), which compares the azimuth/ellipticityangles of the input/output lights in the free-space unit matrix mediagiven input lights with various randomly-selected right- and left-handelliptical polarization states, respectively. It can be seen that inevery case, the azimuth angles and ellipticity angles of the outputlight are in good agreement with the equivalent angles of the inputlight. In other words, the ability of the GA to predict the VR and HPsettings which result in a free-space condition given a randomelliptical polarization state of the input light is confirmed.

Please refer to FIG. 3( d), which verifies a optical compensation of aequivalent free space using a broadband light source such as ASE (1520nm˜1570 nm) FIG. 3( d) shows the linear input polarization lights andthe output light. The average compensation error for azimuth angles andellipticity angles is 0.75° and 1.52°, respectively. A further series ofexperiments was performed to evaluate its feasibility given right-handand left-hand circular input polarization lights, respectively. Theresults presented in Table 2.

Please refer to FIG. 3( e), which compares the azimuth/ellipticityangles of the input/output lights in the free-space unit matrix mediagiven input lights with various randomly-selected right- and left-handelliptical polarization states, respectively. The average compensationerror for azimuth angles and ellipticity angles is 2.1° and 4.7°,respectively. Thus, a free-space condition is successfully achieved.

In addition, the first implementation example is included but notlimited to the five equivalent optical parameters. Any number of opticalparameters sufficient to represent the equivalent of the optical pathmay also be implemented in the present invention.

Please refer to FIG. 4( a), and it is the second better implementationexample for this case. It is the schematic diagram in compensating forfiber coil 406 in order to let fiber coil become a free space unitmatrix 407 in a fiber optic gyroscope. It contains a light source 400, adetector 401, a fiber coupler 402, IOC 403, and fiber coil 406. At oneport of fiber coil, it contains a variable retarder 404 which is used tocompensate for the effect of the effective property of LB in an opticalfiber coil 406, and a half-wave plate 405 which is used to compensatefor the effect of the effective property of CB in an optical fiber 406.A variable retarder 404 and half-wave plate 405 also can be replaced bya polarization controller comprising two quarter waveplates and one halfwaveplate. And its configuration position is not limited to fiber coil406 outlet but can be arbitrary allocated to the optical path betweenIOC 403 and fiber coil 406. All arrangements make the fiber coil becomean equivalent free space. According to this implementation example, if afree-space unit matrix is finally achieved, the input polarizationstates into the compensated fiber coil are exactly same as the outputpolarization states. The light traveling in the fiber coil is just likethe light traveling in air. In addition to the second betterimplementation example, the optical components used to compensate forthe fiber coil 406 are not limited in variable retarder 404 andhalf-wave plate 405 or polarization controller, and any opticalcomponent that can compensate for fiber coil 406 to achieve a free spaceis included.

Please refer to FIG. 4( b), and it is the third better implementationexample for this case. It is the schematic diagram in compensating forfiber coil 406 in order to let fiber coil become a free space unitmatrix 407 in a fiber optic gyroscope. It contains a light source 400, adetector 401, a fiber coupler 402, IOC 403, and fiber coil 406. At theend of fiber coil, twisting part of fiber to compensate for fiber coilis used to make the fiber coil to act like the free space 407. Thetwisted part is not limited to the end of the fiber coil 406 but anyoptical path between IOC 403 and fiber coil 406 is included. And themethod to compensate for fiber coil 406 is not limited in twisting butany method that can make fiber coil 406 become free space 407 isincluded. According to this implementation example, if a free-space unitmatrix is finally achieved, the input polarization states into thecompensated fiber coil are exactly same as the output polarizationstates. The light traveling in the fiber coil is just like the lighttraveling in air.

In conclusion, by means of the compensation method with or withoutadding the optical component, the equivalent free space compensation isaccomplished by the optical system such as fiber optic gyros provided bythe present invention. Besides, the optical verification method isproposed to verify that the polarization state of the input light remainthe same with the output light when the light propagates in thecompensated fiber or fiber component, i.e., the equivalent free space.Therefore, the compensation method of the present invention isparticularly suitable for the fiber sensors applications, such as fibergyros, which greatly enhances the fiber or fiber component repeatabilityand stability throughout the fiber or fiber component production line.

Based on the above descriptions, it is understood that the presentinvention is indeed an industrially applicable, novel and obvious onewith values in industrial development. While the invention has beendescribed in terms of what are presently considered to be the mostpractical and preferred embodiments, it is to be understood that theinvention should not be limited to the disclosed embodiment. On thecontrary, it is intended to cover numerous modifications and variationsincluded within the spirit and scope of the appended claims which are tobe accorded with the broadest interpretation so as to encompass all suchmodifications and variations. Therefore, the above description andillustration should not be taken as limiting the scope of the presentinvention which is defined by the appended claims.

What is claimed is:
 1. An optical verification system for verifying anoptical compensation of an equivalent free space via an optical system,comprising: a broadband light source for emitting a light, an opticalcircuit having an optical fiber or fiber coil is used to input the lightand output the light, wherein the optical circuit has opticalcharacteristics of an equivalent free space via internal or externaloptical compensation; a sample optical component having a given opticalparameter, coupled to the optical circuit; and a polarimeter formeasuring an optical parameter of the output light, wherein the opticalparameter is compared with the given optical parameter to verify thecompensation of an equivalent free space for the optical circuit.
 2. Thesystem as claimed in claim 1, wherein the sample optical component is anoptical component for changing an optical polarization state.